Geodesic
Finite-automaton transformations of strictly almost-periodic sequences
Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 751-756.

Voir la notice de l'article provenant de la source Math-Net.Ru

Different versions of the notion of almost-periodicity are natural generalizations of the notion of periodicity. The notion of strict almost-periodicity appeared in symbolic dynamics, but later proved to be fruitful in mathematical logic and the theory of algorithms as well. In the paper, a class of essentially almost-periodic sequences (i.e., strictly almost-periodic sequences with an arbitrary prefix added at the beginning) is considered. It is proved that the property of essential almost-periodicity is preserved under finite-automaton transformations, as well as under the action of finite transducers. The class of essentially almost-periodic sequences is contained in the class of almost-periodic sequences. It is proved that this inclusion is strict. 
@article{MZM_2006_80_5_a9,
     author = {Yu. L. Pritykin},
     title = {Finite-automaton transformations of strictly almost-periodic sequences},
     journal = {Matemati\v{c}eskie zametki},
     pages = {751--756},
     publisher = {mathdoc},
     volume = {80},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a9/}
}
TY  - JOUR
AU  - Yu. L. Pritykin
TI  - Finite-automaton transformations of strictly almost-periodic sequences
JO  - Matematičeskie zametki
PY  - 2006
SP  - 751
EP  - 756
VL  - 80
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a9/
LA  - ru
ID  - MZM_2006_80_5_a9
ER  - 
%0 Journal Article
%A Yu. L. Pritykin
%T Finite-automaton transformations of strictly almost-periodic sequences
%J Matematičeskie zametki
%D 2006
%P 751-756
%V 80
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a9/
%G ru
%F MZM_2006_80_5_a9
Yu. L. Pritykin. Finite-automaton transformations of strictly almost-periodic sequences. Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 751-756. http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a9/

[1] M. Morse, G. A. Hedlund, “Symbolic dynamics”, Amer. J. Math., 60 (1938), 815–866 | DOI | MR | Zbl

[2] M. Morse, G. A. Hedlund, “Symbolic dynamics II: Sturmian trajectories”, Amer. J. Math., 62 (1940), 1–42 | DOI | MR | Zbl

[3] An. Muchnik, A. Semenov, M. Ushakov, “Almost periodic sequences”, Theoret. Comput. Sci., 304 (2003), 1–33 | DOI | MR | Zbl

[4] A. Weber, “On the valuedness of finite transducers”, Acta Informatica, 27 (1989), 749–780 | MR